We revisit the following problem: Given a convex polygon P, find the largest-area inscribed triangle. We prove by counterexample that the linear-time algorithm presented in 1979 by Dobkin and Snyder [5] for solving this problem fails, as well as a renewed analysis of the problem. We also provide a counterexample proving that their algorithm fails finding the largest-area inscribed quadrilateral. Combined with the work in [2], [3], it follows that the algorithm is incorrect for all possible values of k.

中文翻译：

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再看凸多边形中的最大面积三角形

我们重新审视以下问题：给定凸多边形P，找到面积最大的内接三角形。我们通过反例证明，Dobkin和Snyder [5]于1979年提出的线性时间算法无法解决该问题，并且对该问题进行了重新分析。我们还提供了一个反例，证明他们的算法无法找到最大面积的内接四边形。结合[2]，[3]中的工作，得出的结论是该算法对于k的所有可能值都是错误的。